Determining subterranean reservoir properties is an important function for a wide array of applications, such as the production of minerals, e.g., oil and gas, groundwater technology and modeling contaminant transport in the subsurface. These properties include the permeability, wettability, porosity and grain size of the rocks, as well as the large scale flow patterns in the rock formations. The present invention lends itself to all of these areas.
The permeability of a material is a measure of the ability of a porous medium to transmit fluids through its pore spaces. For sufficiently slow, linear, incompressible steady flow it is described by Darcy's law: ##EQU1## where K=permeability, darcys (d),
q=flow rate, cc/sec, PA1 .mu.=fluid viscosity, centipoise (cp), PA1 L=sample length, cm, PA1 .DELTA.P=fluid pressure differential across the sample, atmospheres (atm), PA1 A=sample cross-sectional area perpendicular to flow direction, cm.sup.2.
The most commonly used permeability units are the "darcy" (d) and "millidarcy" (md). A rock having one darcy permeability conducts 1 cc/sec volume of 1 cp viscosity fluid through a cubic sample having 1 cm length sides under a pressure differential across the sample of 1 atm. Normally, permeability is determined by taking core samples from the reservoir and carrying out well defined measurement techniques, well known to those skilled in the art, on the samples. Several such techniques available for making these measurements are described in PETROLEUM PRODUCTION ENGINEERING - DEVELOPMENT by L. C. Uren, Fourth Edition, McGraw-Hill Book Company, Inc., 1956 and in American Petroleum Institute, API RECOMMENDED PRACTICE FOR CORE-ANALYSIS PROCEDURE, API RP 40, 1960.
More particularly, permeability plays a very important role in describing the fluid flow in oil and gas reservoirs. Two primary methods of measurement are practiced in the industry: steady state method and the dynamic displacement method. In each a cylindrical core is first saturated with water or brine and then oil flooded to irreducible water saturation. The core is then water flooded or brine flooded and the pressure drop across the core is measured along with the oil or water or brine production. The average saturations within the core are determined from the overall material balance. However, the steady state method requires lengthy measurement times since it requires stabilization of the fluid flow; while the dynamic displacement method does overcome this, it suffers from capillary end effects, and is therefore only effective for high flow rates.
Both of the above described methods of measuring permeability are additionally limited in the information they provide. Specifically, both methods provide only the average or bulk permeability for the core, and can only achieve a resolution on the order of about an inch or so, where core diameters are in the range of 1 inch to 4 inches. Additionally, it is well known that permeability can vary considerably in sandstones over a distance of only one or two millimeters. The degree of variation in permeability has justifiably received much attention in recent years. Information about permeability variation within a formation can provide valuable information about the geological characteristics of the formation. This information is useful in predicting how an oil field will develop, the yields that can be expected, and how it might compare or contrast with already known and developed fields. Running flooding permeability tests, as described above, on very small diameter cores is not an acceptable solution to the problem, since the permeability can still vary considerably along the length of the core. Furthermore, running flooding tests on small diameter, small length cores is not practical because of hydraulic sealing problems and problems introduced by boundary effects.
The only known method that employs light transmission for estimating permeability is by examination of thin sections of the core. Thin sections of geologic samples less than 60 .mu.m thick are customarily examined with petrographic image analysis techniques to study the micro-features of the sample. From this analysis, geological interpretations of the depositional and post depositional process which formed the sample can be derived. Moreover, physical qualities such as the porosity and permeability of the sample can be estimated. The permeability of the sample, which depends on an interconnected network of individual pores, can be estimated from the porosity of the sample by a linear regression formula or by the empirical Kozeny-Carman equation. Since a thin section has no meaningful permeability itself, the above method gives only an indirect and qualitative estimate of the permeability of the parent volume of rock from which the sample was derived.
A need thus exists for a method to directly measure the permeability and permeability variation in a core having a macroscopic thickness (i.e. a thickness of many layers of grains), with resolution on the order of millimeters. There have been some efforts to obtain permeability measurements in the "less-than-bulk, greater-than-microscopic" range, but most proposed methods are time consuming and cumbersome. For example, Chandler, et al. in their article, "A Mechanical Field Permeameter for Making Rapid, Non-Destructive Permeability Measurements," J. Sedimentary Petrology, 59, 613 (1989), discuss an apparatus (an "air minipermeameter") which achieves a resolution on the order of 2 cms. While this is an improvement over the bulk method, it can still overlook important variations on the millimeter level. Swanson, in his article "A Simple Correlation Between Permeabilities and Mercury Capillary Pressures," J. Petroleum Tech., 33, 2498 (1981), discusses a method for determining the permeability of tiny chips of rocks using mercury injection porosimetry. While this method may provide the desired resolution, it is cumbersome and does not provide for a continuous plot or "map" of the permeability and its variation across the core.
The problem of wettability, of great interest in petroleum production problems, concerns knowing when two fluids (e.g., oil and water) and present in the rock pore space, which fluid adheres to, or "wets", the pore walls or the surface of the rock grains, while the non-wetting fluid occupies the voids between the grains or the pores. The importance and application of this problem is discussed in "Application of Capillary Pressure Measurements to the Determination of Connate Water Saturation," by N. R. Morrow and by J. C. Melrose in Interfacial Phenomena in Petroleum Recovery (N. R. Morrow, ed., Marcel Dekker, N.Y., 1991). At present there exists no non-invasive, non-destructive method by which one can determine whether oil or water wets the surface of the rock grains when both fluids are present.
While the permeability of a rock contains information about the grain size, in petrophysical studies it is of fundamental importance to make measurements of the grain size itself. This parameter can be determined from either microscopic measurements, or by measuring with sieves of known grid sizes upon disaggregating the rock into the constituent grains. Alternately, apparatus are commercially available which can determine the grain size of a rock sample by use of a laser. One such apparatus is sold under the name MICROTRACR.RTM. by Leeds & Northrup Co. Operation of this apparatus is described in detail in "Rapid Analysis of Submicron Particles," by P. E. Plantz and H. N. Frock. This apparatus requires a sample of the composite medium to be disaggregated, the particles are then blown in a cloud through a laser beam, with the resulting scattering effect of the laser being correlatable to the particle size. This effect is also discussed in "Measurement of size and concentration of scattering particles by speckle photography" by Genceli, et al., J. Opt. Soc. Am., V70, 10, 1212, wherein the authors admit, "there are moderate restrictions on the number of particles per unit volume."
The permeability of rocks may be affected by the reaction of clays within the rock. Typically, in their natural state within a subterranean formation, clays are compacted around the grains of the rock. Once the natural source fluid is replaced with another fluid, the clays may swell, plugging the channels connecting the pores, and lowering permeability. It is desirable to know not only the total change in permeability, but also the rate at which permeability changes. Current means in the art for determining the effect that different fluids may have on permeability require flooding the core with the various fluids and measuring the bulk permeability. In this manner, however, data can only be collected at various times, rather than in a continuum. Furthermore, it is difficult to determine, with this method, precisely how the permeability may be changing as a function of time.
Previous methods of optically characterizing cores have concentrated on reflected light. Herbin, et al. disclose In U.S. Pat. No. 4,852,182 a method of longitudinally splitting a core and imaging the cross section by reflected normal light. Along a similar vein, Pruett, et al. in U.S. Pat. No. 4,616,134 disclose a method and apparatus for optical surface scanning of longitudinal cores. However, neither of these methods actually measures properties of the core, other than its variation in color.
Recent advances in imaging technology have been applied to the area of geologic samples. For example, Smith in U.S. Pat. No. 4,797,906 teaches a method to measure porosity in thin sections by use of X-ray reflectance to stimulate naturally occurring fluorescence in the sample. NMR (Nuclear Magnetic Resonance) has been used in U.S. Pat. No. 4,728,892 wherein Vinegar, et al. teach a method for determining, among other petrophysical properties, permeability by indirect calculation from measured porosity. Vinegar et al. state that a high resolution (1 mm) can be obtained with NMR imaging, however, the method is limited to cores 4.2 cm or less in diameter. In U.S. Pat. No. 4,868,751 Dogru, et al. claim a method for determining permeability that combines the classic method of confining the core to a pressure sleeve with the technology of CAT (Computer Aided Tomography) scanning during the flooding. Dogru, et al's method purportedly eliminates capillary effects on permeability in the core, but does not indicate that the method gives a high resolution image of the variation in permeability within the core. None of the methods either teach or suggest the use of light transmission through the sample to measure permeability.
The porous media that are the focus of this invention are non-absorptive to light. A good example of an absorptive material is a thin film of black plastic; while the medium is very thin, no light passes because it is absorbed by the medium. In non-absorptive materials, light might be expected to transmit through the medium and emit from the other side, which it does in many cases. However, in some instances some or all of the light which is transmitted into the non-absorptive medium may not be transmitted through the medium due to diffusion of the light inside the medium. A good example of this latter category is a dense pack of irregular quartz crystals not unlike sandstone.
Light transmission through composite media is a subject that has received much attention recently. Current theories and studies of the phenomenon concentrate on the scattering of laser light within the medium in order to study the mechanism of propagation. Typically, the medium is a smoke or vapor or particles suspended in a fluid, gel or solid with particle densities so low that normally occurring light can easily pass through. (e.g., Ishimaru, Kuga, et al., "Scattering and Diffusion of a Beam Wave in Randomly Distributed Scatters," J. Opt. Soc. Am. 73, 131-136, 1983). Other studies have considered the phenomenon of light transmission through a porous bed of spherical glass, as for example Gate, "The Determination of Light Absorption in Diffusing Materials by a Photon Diffusion Model", J. Phys. D.: Appl. Phys., 4, 1049-1056, 1971 (Great Britain). In these studies, the porous media have been transparent to visible light, and so the propagation of laser light through them is not surprising. The concept of laser light transmission through media normally opaque to light was considered and discussed in a paper by Anderson, "The Question of Classical Localization--A Theory of White Paint?", Philosophical Magazine B, 52, 3, 505-509, 1985. In his paper Anderson theorized a slab of thickness W of material containing random non-absorptive scatters embedded between two non-random propagating media. Stating that if the slab is thick compared with the conventionally defined mean-free-path 1, coherent radiation will be exponentially attenuated, Anderson went on to state that most of the incident radiation will be scattered diffusely and, since it has been postulated that there is no absorption, the radiation must all come out on one side or the other of the slab W. Thus there is a clear distinction between the transmission of diffuse, incoherent radiation of a "localized" system and an "extended" system, once the system is sufficiently large. Unfortunately, "sufficiently large" also means "sufficiently opaque" and the experimental problem may not be all that simple according to Anderson, therefore optimum scattering requires structures comparable to the wavelength (i.e., particle diameter is approximately equal to wavelength). In addition, although great complexity may be encountered, the work may impinge on a number of highly interesting and practical systems, such as porous media. This therefore indicates that light transmission through a non-absorptive porous medium such as a macroslab of sandstone, as described herein, is not to be expected at all, since in sandstone the wavelength of a laser light is much less than the particle diameter, and the macroslab, due to its thickness, is sufficiently opaque.
Others have additionally theorized about light transmission in rock. In a paper titled, "Reflectance and Albedo Differences Between Wet and Dry Surfaces", Twomey, et al., Applied Optics, 25, 3, 431-437, 1986, the authors discuss why light is preferably absorbed by wet rock over dry rock. The theories developed in this paper suggest that forward light scattering into porous media is dependent on the type of fluid present in the voids. However, the focus of the article is absorption by the media rather than transmission by the media, and no speculation is made as to light continuing to propagate through the media, or that the amount of light transmitted into (i.e., absorbed by) the media might be correlated to the overall permeability of the media.
In petroleum production problems and groundwater studies, it is necessary to predict fluid flow characteristics in a stratified earth, where the permeabilities of the various strata are known or given. Such characteristics are usually determined from computer simulations. In conjunction with such simulations, it is useful to have a scale-model laboratory "reservoir" where the predictions of the simulation can be verified. Thus, what is needed in the art is a simple, non-destructive, non-invasive, effective method for determining various properties of a porous medium. Such properties include permeability, grain size, wettability, porosity and clay swelling of a porous medium, as well as the absence or presence of fluid in the porous medium, type of fluid present, and scale modelling of fluid flow patterns in a stratified porous medium. We have recently discovered that laser light will be transmitted through a macroslab of sandstone, on the order of 1 mm to 20 mm thick, preferably 5-10 mm thick. A phenomenon not expected since such a slab is ordinarily opaque to visible light. We have further determined that the amount of light transmitted through the macroslabs is correlated to the permeability of the slab at the point of transmission. Additionally, we have discovered that the laser transmission through a consolidated sandstone allows for determination of average grain size where the sandstone has a high concentration of particles per unit volume; thereby allowing a nondestructive measurement of said grain size. We have still further discovered that the transmission of the laser light through a macroslab containing water and white oil is dependent upon which of the two fluids wets the grain surface, and allows for a method for continuously monitoring the change in permeability with respect to time in a macroslab core section flooded with various fluids. Finally, it has been found that use of the transmission phenomenon allows for prediction of fluid flow characteristics when used in conjunction with computer simulation, wherein scale model reservoirs are constructed so that light transmission in said models can be observed and measured.